Question

the Time between two arrivals in a queuing model is normally distributed with mean 2 minutes and standard deviation 0.25 minutes if random samples of size 36 are drawn what is the probability that the sample mean will be less then 2.25 minutes ?

Answer 1

$\mu=2 \\ \sigma=0.25 \\ n=36 \\ P(\bar{x}<2.25) = P(Z< \frac{2.25-2}{0.25/ \sqrt{36}}) \\ = P(Z<6) \\ = 0.9999$